Step 1: Calculate the required equity

Your required equity is how often you will need to win the pot at showdown in order to make a call profitable.

Required equity = price of calling / (pot size + price of calling)

Price of calling: The difference between your last raise and the all-in.

Pot size: All the money you can win. Your raises, your opponent's all-in, the blinds.

Remember that you can only win as much money from others as you can put in the pot yourself. So if your opponent shoves all-in for 200BB and you only have 100BB, you will only be able to win 100BB from him.

In this case, you need 40% equity to make a call profitable. You can find the exact calculation if you click on the spoiler.

Your required equity is always below 50%. This is because the price of calling is represented at least twice in the denominator of the formular. If the pot size was 0 before your opponent bets, then the pot size would be equal to the price of calling and we would have:

Required equity = price of calling / (price of calling+ price of calling) = ½ = 50 %. However, since the pot always contains at least the blinds, the required equity will always be below 50%.

Step 2: Put your opponent on a range

The following range is a good starting point, since many opponents will go all-in with these hands in the given situation: JJ+, AK

Step 3: Calculate your equity against your opponent's range

Since you are holding QQ in this spot, you have 47% equity against your opponent's range (JJ+, AK). That is more than the required equity of 40%, so you should call.

If AK was not in your opponent's range, that is if he would only go all in with JJ+, your equity against that range would be exactly 40%. That would be almost exactly the same amount as the required equity. A call would break even and thus be unprofitable considering the rake.

If your opponent would only shove all in with QQ+ and AKs, you would only have 29% equity when holding QQ. That is less than the required equity of 40%, so you should fold.

If you hold instead of , your opponent's bluffing range on the river now consists of three combos instead of 12. Against that range you only have 26% equity, which is considerably less.

So you should fold, despite the fact that your absolute hand strength is actually stronger. The basis of your decision should always be relative hand strength, that is the equity of your hand against the range of your opponent.

Summary

If you are facing an all-in or a river bet, you should follow three steps to decide whether to call or to fold:

It's supposed to be done after a session to sharpen your in-game intuition help you to focus on getting your opponent's ranges correct in set situations and work out whether you are making moves that will give you a profit vs your opponents ranges in the long term. Also using the combinatrics you can work out if perhaps you are being to passive or too aggressive with specific holdings vs specific opponents on specific boards.

To answer C101,the opponent's range changes when you hold AQ because it states in the example that Villain could be bluffing with a busted A-high flush draw. However, since you are holding the A needed to complete his flush draw, it then eliminates all of Villain's bluffs with any A-high flush draw he may have been holding.<br />
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Not so complicated once you get around the math behind it. It's essentially just calculating your pot odds and then comparing the strength of your hand vs Villain's range of hands to figure out if you are ahead, behind, or can outdraw him profitably over the long term.

very good explaining i seen, i tried understand the equity and notation from different source, but here its like lightning in clear sky.<br />
Only bad thing about site so far it wont let me do this test...hopefully temporary problem.